problem 201

[lisyuan]

I am really confused with this problem. The question is :


If the sum of n consecutives is o, which is the following must be true.

1. n = even
2. n = odd
3. the average of n integer is 0.

The answer of 2 & 3 must be true, and I don't see why n= odd

In order for the average = 0

the sum of number has to be 0.

sum of numbers/number of numbers = average

is the sum = 0, then the average is 0

in order for that to happen, we need equal number of same number with opposite signs to cancel each other, for example(-3)+(-2)+(-1)+(0)+(1)+(2)+(3), i can also have (-4)+(-2)+0+(2)+(4)

then the sum being odd number or even number would be irrelevent, right?

Then, why the official answer should be 2 &3?

Thanks!!!

[reachac]

I'll use a piece from ur post only,

in order for that to happen, we need equal number of same number with opposite signs to cancel each other, for example(-3)+(-2)+(-1)+(0)+(1)+(2)+(3), i can also have (-4)+(-2)+0+(2)+(4)

does the part in bold represent consecutive integers??

[pepeprepa]

You just bug a little
As you explained if you want the consecutive sum to be equal to 0 you can have (-3)+(-2)+(-1)+(0)+(1)+(2)+(3), i can also have (-4)+(-2)+0+(2)+(4)
They do not ask you if the numbers are odd or even, they ask you if "n" is odd or even. In your examples n=7 and n=5

[yvichman]

-4,-2,0,2,4 are not consecutive. they skip numbers in between.

also N will always be odd, b/c you will always have zero as the median to get the the sum of consecutive numbers equal zero.